# Example for full simulation loop using the multi target mode for custom analytic
functions

This example shows how to use a multi target objective for a custom analytic function.
It uses a desirability value to handle several targets.

This example assumes basic familiarity with BayBE, custom test functions and multiple
targets.
For further details, we thus refer to
- [`campaign`](./../Basics/campaign.md) for a more general and basic example,
- [`custom_analytical`](./custom_analytical.md) for custom test functions, and
- [`desirability`](./../Multi_Target/desirability.md) for multiple targets.

## Necessary imports for this example


```python
import os
```


```python
import numpy as np
```


```python
from baybe import Campaign
from baybe.objectives import DesirabilityObjective
from baybe.parameters import NumericalDiscreteParameter
from baybe.searchspace import SearchSpace
from baybe.simulation import simulate_scenarios
from baybe.targets import NumericalTarget
```

## Parameters for a full simulation loop

For the full simulation, we need to define some additional parameters.
These are the number of Monte Carlo runs and the number of experiments to be conducted
per run.


```python
SMOKE_TEST = "SMOKE_TEST" in os.environ
```


```python
N_MC_ITERATIONS = 2 if SMOKE_TEST else 5
N_DOE_ITERATIONS = 2 if SMOKE_TEST else 4
BATCH_SIZE = 1 if SMOKE_TEST else 2
DIMENSION = 4
BOUNDS = [(-2, 2), (-2, 2), (-2, 2), (-2, 2)]
POINTS_PER_DIM = 3 if SMOKE_TEST else 10
```

## Defining the test function

See [`custom_analytical`](./custom_analytical.md) for details.


```python
def sum_of_squares(*x: float) -> tuple[float, float]:
    """Calculate the sum of squares."""
    res = 0
    for y in x:
        res += y**2
    return res, 2 * res**2 - 1
```

## Creating the searchspace

In this example, we construct a purely discrete space with 10 points per dimension.


```python
parameters = [
    NumericalDiscreteParameter(
        name=f"x_{k+1}",
        values=list(np.linspace(*BOUNDS[k], POINTS_PER_DIM)),
        tolerance=0.01,
    )
    for k in range(DIMENSION)
]
```


```python
searchspace = SearchSpace.from_product(parameters=parameters)
```

## Creating multiple target object

The multi target mode is handled when creating the objective object.
Thus we first need to define the different targets.
We use two targets here.
The first target is maximized and the second target is minimized during the optimization
process.


```python
Target_1 = NumericalTarget(
    name="Target_1", mode="MAX", bounds=(0, 100), transformation="LINEAR"
)
Target_2 = NumericalTarget(
    name="Target_2", mode="MIN", bounds=(0, 100), transformation="LINEAR"
)
```

## Creating the objective object

We collect the two targets in a list and use this list to construct the objective.


```python
targets = [Target_1, Target_2]
```


```python
objective = DesirabilityObjective(
    targets=targets,
    weights=[20, 30],
    scalarizer="MEAN",
)
```

## Constructing a campaign and performing the simulation loop


```python
campaign = Campaign(searchspace=searchspace, objective=objective)
```

We can now use the `simulate_scenarios` function to simulate a full experiment.


```python
scenarios = {"BayBE": campaign}
```


```python
results = simulate_scenarios(
    scenarios,
    sum_of_squares,
    batch_size=BATCH_SIZE,
    n_doe_iterations=N_DOE_ITERATIONS,
    n_mc_iterations=N_MC_ITERATIONS,
)
```

    

    

    

    



```python
print(results)
```

      Scenario  Monte_Carlo_Run  Iteration  Num_Experiments Target_1_Measurements  \
    0    BayBE                0          0                1                [12.0]   
    1    BayBE                0          1                2                [16.0]   
    2    BayBE                1          0                1                 [8.0]   
    3    BayBE                1          1                2                [16.0]   
    
      Target_2_Measurements  Target_1_IterBest  Target_1_CumBest  \
    0               [287.0]               12.0              12.0   
    1               [511.0]               16.0              16.0   
    2               [127.0]                8.0               8.0   
    3               [511.0]               16.0              16.0   
    
       Target_2_IterBest  Target_2_CumBest  
    0              287.0             287.0  
    1              511.0             287.0  
    2              127.0             127.0  
    3              511.0             127.0